Question

-12r + 28 ≤ -4(2r - 13)
A) {r | r > -6}
B) {r | r ≥ -6}
C) {r | r ≤ -6}
D) {r | r < -6}

I believe it is C, but can anyone double check? The direction of the sign always confuses me.

Answer 1

I don't think it's C. Can you show your work and we'll see where the error is?

Answer 2

Yes, Hold on one sec.

Answer 3

In the last step, you divided both sides of the inequality by -4. What do you have to do when you multiply or divide by a negative number?

Answer 4

(I can't help but notice that you didn't write the inequality symbol in that step anymore, lol)

Answer 5

:) Thats because the only thing I don't understand is when and when not switch the direction of the sign. I can get the answer, I just don't know when to switch the sign,

Answer 6

OK, let's get you over that little hump. :)

Solving an inequality is JUST LIKE solving an equation. the only thing you need to remember is that, if you MULTIPLY or DIVIDE by a NEGATIVE NUMBER, then you must SWITCH THE DIRECTION of the sign.

That's it! Switch, ONLY if, you mult or divide by a negative.
NOT if you add or subtract stuff.
NOT if you mult or divide by a POSITIVE number.

WHY? think about it:

-3<4 Now multiply both sides by -2:
6>-8 right???

But: if I have -3<4 and I multiply by +2, I just get -6<8. Still true. Try it with some different simple numbers, the ONLY time the sign needs to flip, is if you....

....what?.....
.... SAY IT WITH ME:

MULTIPLY OR DIVIDE BY A NEGATIVE NUMBER.

:)

Answer 7

So then this one would be B, because I'm dividing 24 by a negative 4?

Answer 8

Sorry... stepped away from the computer. :) Yes, it would be B. Not so much "because you divided by a negative 4", but because that's how the solution works out.

What I mean is, notice that if you ADDED the 12r to both sides and SUBTRACTED 52 to both sides, then you would have never had a negative coefficient on the r, and would have divided by +4 in the final step, so no flipping of the inequality. BUT, the r term would be on the other side of the inequality, so you would still end up with the same solution, r>=-6.

E.g., just from a strategic point of view, sometimes the side you move the variable terms to can avoid that negative division. But it won't change the answer!

If I have:

2x-3>-4x+1 and I subtract the 2x and subtract the 1:
-4>-6x Now divide by negative so flip the sign:
4/6<x
2/3<x or I can write that x>2/3

Now instead if I have:

2x-3>-4x+1 and I add the 4x and add the 3:
6x>4
x>4/6
x>2/3

See, same thing, and I never had to flip!

Answer 9

Thanks Debbie! :)

Answer 10

You're welcome, happy to help. :)